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LC reductions yield isomorphic simplicial complexes. (English) Zbl 1191.52011
Summary: We say that a vertex \(v\) of a finite simplicial complex \(K4\) is LC-removable if the link of \(v\) is a cone, and that \(K\) is LC-irreducible if it has no LC-removable vertices. Answering a question of Y. Civan and E. Yalcın [J. Comb. Theory Ser. A 114, No. 7, 1315–1331 (2007; Zbl 1126.05046)], we prove that all LC-irreducible simplicial complexes that can be obtained from a given \(K\) by repeatedly deleting LC-removable vertices (plus all simplices containing them) are isomorphic.

52B99 Polytopes and polyhedra
05E99 Algebraic combinatorics
55U10 Simplicial sets and complexes in algebraic topology
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